Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C64×C79 ⋊ C2 |
| Sylow | C79 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C2×D79 |
| commutator, socle | C2×C79 | C2×C32 |
| Fitting | C64×C79 | C2 |
| prime radical | C2×D79 | C32 |
| cosocle | C32×C79 | C22 |
| hypercenter | C64 | D79 |
| hypocenter | C79 | M128 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M128×D79, C2×#23761610, #34209307, … |
| maximal normal subgroup of | M128×D79, C2×#23761610, #34209307, … |
| maximal quotient of | #34176073, (C2×D79)⋊C64, Dic79⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2720);